The problem of creep induced instability in structures is discussed. A linearization procedure proposed by Onat and Wang (Creep in Structures, Springer-Verlag, 1962, p. 125) and generalized by Carlson (Recent Progress in Applied Mechanics - The Folke Odgvist Volume, Almqvist and Wiksell, Gebers, Stockholm, 1966) is applied to the problem of the creep buckling of circular cylindrical shells under uniform, axial compression. Solutions for axisymmetric creep buckling of semi-infinite and infinite cylinders are obtained and a comparison with experimental data is made. In accordance with expectations based on the criterion for instability, the theoretically predicted critical times are smaller than the experimentally observed critical times.